Energy balance of the mixture

We shall now recalculate the energy of mixing of Aa molecules of A and Ab molecules of B in that context of local composition, by finding the energy balance of that mixture. We suppose that in pure liquid A, a molecule 

The interaction between two molecules that are not immediate neighbors 

In order to extract a molecule of A from the pure liquid A, we must break Za A-A bonds and therefore provide the energy za aa- We place that molecule in the pure liquid B. This transfer forms new bonds and therefore releases the energy z a ( aa aa +Tba ba) The variation in energy due to the transfer of a molecule of A from the pure liquid A into liquid B will therefore be Za aa z a (yAA AA+ yBA sA) Obviously, we can calculate a symmetrical expression for the transfer of a molecule of B from liquid B into liquid A. The variation in internal energy to form a mole of mixture, therefore, will be  

Taking accoimt of relations [3.50a], [3.50b], [3.53] and [3.54], we find the following for the excess- or mixing molar internal energy  

Based on our knowledge of the internal mixing energy, we calculate the Helmholtz energy using the relation  

---